The beaches of Tel Aviv are busy, the cafes along the sea-front do brisk business. Gaza is just a few miles to the south, but it's a world of horror far removed.

And a war fought at arms length is for Israel a war they're happy to pursue for however long it takes.

The government here talks about the terror of Hamas rockets. The threat is real but at the same time largely psychological.

Smoke billows from Shejaia after shelling on the neighbourhood intensified. Credit: Reuters

The civilian death toll from direct Hamas fire stands at two. In Gaza, as I write, more than 370 are said to have died. Many of them children, many of them women; a minority actually Hamas fighters.

Overnight, the Israelis have launched their heaviest bombardment yet. Troops are pushing deeper into that narrow strip of coastal land. A peace deal is as close and as elusive as ever.

Thousands are fleeing the attacks on Shejaia, packing a nearby hospital. Credit: Reuters

It's as if the diplomatic wheels are turning, but the cogs are not engaging. It doesn't help that there are two peace processes in play.

The Egyptian-sponsored deal, accepted last week by Israel, the Arab League and the Palestinian Authority but rejected by the Hamas leadership in exile. Then there's a second track - pushed by Qatar and Turkey.

This has Hamas support but lacks wider traction. Ban-Ki-Moon and the Palestinian President Mahmoud Abbas are in Doha today to try to forge a common approach. In Israel there's little appetite to stop a war many feel is long overdue.

Israeli police and members of the media take cover as the Iron Dome intercepts Hamas rockets. Credit: Reuters

I spent two days in the town of Ashkelon this week, close to the Gaza border, where the siren call of rocket attack and the whoosh of Iron Dome defence missiles flying through the sky have become wearyingly routine.

While we were there, alarms sounded every few hours. People left their café tables to take cover in the shade of the shop fronts. When the sirens ceased, they'd emerge, angrier than ever.

Cross-border air strikes from Israel have continued during the ground invasion. Credit: Reuters

Here, they wanted their troops to finish Hamas I remember the woman, in her mid-thirties, who wanted to tell me that the fear of Hamas rockets, over many years, meant people lived every day with a constant if low level of anxiety for their lives.

"This must not end until Hamas is destroyed,'' she said. And then she went back to her shopping.